工学部_研究紹介_2019_英語版

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OkamotoLabNonlinear Partial Differential EquationsManyphysical,chemical,andbiologicalphenomenacanbemodeledusingdifferentialequations,whichareinmanycasesnonlinear.But,itisdifficulttofindasolutionoftheCauchyproblem(initialvalueproblem)fornonlinearpartialdifferentialequations(PDEs)becauseofitsnonlinearity.Well-posednessoftheCauchyproblemthereforeisimportantandafirststepofstudyfornonlinearPDEs.Here,well-posednessmeansthattheexistenceofasolution,uniqueness,andcontinuousdependenceofinitialdata.MamoruOkamotoAssistant ProfessorHe received doctor's degree of science from Kyoto University.His research interest is nonlinear partial differential equations.Ouraimistoobtainlowregularitywell-posednessoftheCauchyproblemfornonlinearpartialdifferentialequations(PDEs),especiallynonlineardispersiveandwaveequations.Ifnonlinearpartshavesymmetry,namelyisinvariantundersometransformations,onecanexpectthattheworstinteractioniscancelledout.ConstructionofatheoryforthesecancellationpropertiesisourgoalandthatwillcontributetheevolutionofawiderangeofnonlinearPDEs.Inordertomoreadvancedresearch,somegraduatedstudentsofourlaboratoryenteragraduateschool.Otherstudentsfindajobincompanies.In seminars, besides understanding mathematical statements, good presentation skills are also required.In the FutureAfter GraduationEngineering Core SuzukiLabMycurrentresearchinterestfocusesonthespectraofelectronsinhydrogenatedgraphenes.Grapheneisananomaterialcomposedofcarbonatomsthatarearrangedinatwodimensionalhoneycomblattice.Whilegrapheneisasemiconductorwithzerobandgap,fullyhydrogenatedgraphene,whichisinparticularcalledgraphane(withana),isaninsulatorwithabandgap.Iaminterestedinthespectraofelectronsinpartiallyhydrogenatedgraphenes.SUZUKI,AkitoAssociateProfessorResearchInterests:MathematicalPhysics,SpectralAnalysisKeywords:QuantumFieldTheory,DiscreteLaplacianMathematical Physics :Mathematics sheds light on physical phenomenaMathematics Thestructureofsuchamaterialismathematicallydescribedbyagraphthatiscomposedofthesetofverticesandedges.Atomsinthematerialaredescribedbytheverticesandatomicbondsbytheedges.ThentheLaplaceoperatoronthegraphbecomestheHamiltonianofanelectronmovinginthematerial.ThespectrumofthisHamiltoniancorrespondstotheenergyoftheelectron.Thephysicalpropertieslikeelectricalconductivityareanalyzedviaspectralanalysisbymathematicssuchasfunctionalanalysis,operatortheoryandgraphtheory.Tostudythespectraofelectronsisanimportantprobleminmathematicalphysics.70